This invention relates to diffractive optical elements, and more particularly to a method to synthesize amplitude and phase weights for desired diffractive patterns for optical elements in applications using phase-only spatial light modulators (SLM) and diffractive optical elements, their mathematical design, physical realization and fabrication procedure.
Phase errors can profoundly distort the intended diffraction patterns of spatial light modulators (SLMs) thus impacting the performance of optical processing systems that use SLMs. Phase errors are introduced by a variety of mechanisms. Phase-modulating SLMs can have inherent phase errors, due to fabrication process variations from pixel to pixel. Noise (e.g. thermal, quantization, etc.) on the video signals modulating SLMs is also transformed into phase errors. Furthermore, many applications, including composite filters for pattern recognition, binary diffractive optics and optical neural networks, can often be better understood and analyzed by modeling the modulations/signals as random, rather than as deterministic. This viewpoint has led to the invention/development of statistically based methods of design and new devices that arise from these design methods. This is the subject of this invention.
Random phase modulations across the surface of the SLM diffract into broadly spread noise patterns. These noise patterns not only have the appearance of speckle patterns, but in fact, arise from the identical situation of scattering of light from a random surface. There is a wealth of information on laser speckle (J. C. Dainty, Laser Speckle and Related Phenomena, Springer, 1984) and statistical optics (J. W. Goodman, Statistical Optics, Wiley, 1985) that is applicable to SLM-based optical processors. This invention was motivated by the opinion that speckle theory could be applied to advance the performance of optical processors that use SLMs and to lead to new applications of SLMs. More specifically, the present invention is an improvement on the technology of the following U.S. patents, the disclosures of which are incorporated herein by reference: U.S. Pat. No. 4,588,260 issued to Horner;
U.S. Pat. No. 4,765,714 issued to Homer; PA1 U.S. Pat. No. 5,363,186 issued to Cohn and Liang; and PA1 U.S. Pat. No. 5,276,636 issued to Cohn.
Both of the Cohn and Homer patents deal with SLM technology, and Cohn uses pseudorandom encoding of SLM systems. Improvements in diffraction efficiency, uniformity and signal-to-noise ratios is possible with the improvements to pseudorandom encoding (including partial encoding) of spatial light modulators that are described in this invention.
Traditional theories of speckle generation by rough surface scattering are adapted to analyzing SLMs. SLMs are modeled as arrays of sub apertures/pixels that are perturbed by random phase components. While traditional speckle theory models random surfaces as stationary random processes, SLMs can be programmed to produce nonstationary optical surfaces. This generalization is used to devise a new class of computer generated holography algorithms, referred to as pseudorandom encoding. The method is notable in that it 1) uses all available space bandwidth of the SLM; 2) produces diffraction patterns having large signal to noise ratio; and, most notably, 3) can be calculated in real-time by serial processors.